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In this article, we propose a Trajectory Reconstruction Model as an improvement to existing speed-based travel time estimation models. The proposed model utilizes point-based speed data collected by existing Intelligent Transportation Systems (ITS). Using the smoothing scheme proposed, it is possible to construct a speed surface as a function of space and time. Then, one can reconstruct the trajectory of an imaginary vehicle by allowing it to adopt the local speed determined by the speed surface wherever the vehicle travels. Therefore, the travel time of this vehicle can be readily determined from its trajectory. This article develops an analytical formulation of the model. Meanwhile, a discrete version of the formulation is also provided as a computational algorithm to facilitate real world implementation. In comparison with existing models, the proposed model accounts for continuous speed variation in both time and …